Log-concavity Results on Gaussian Process Methods for Supervised and Unsupervised Learning

@inproceedings{Paninski2004LogconcavityRO,
  title={Log-concavity Results on Gaussian Process Methods for Supervised and Unsupervised Learning},
  author={Liam Paninski},
  booktitle={NIPS},
  year={2004}
}
Log-concavity is an important property in the context of optimization, Laplace approximation, and sampling; Bayesian methods based on Gaussian process priors have become quite popular recently for classification, regression, density estimation, and point process intensity estimation. Here we prove that the predictive densities corresponding to each of these applications are log-concave, given any observed data. We also prove that the likelihood is log-concave in the hyperparameters controlling… CONTINUE READING

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